Do Now (partner #1)

• p: you live in San Francisco• q: you live in California

1) Conditional Statement2) Contrapositive Statement3) Converse Statement4) Inverse Statement5) Is the statement Biconditional?

Do Now (partner #2)

• p: two angles are complementary.• q: the sum of their measure is 90.

1) Conditional Statement2) Contrapositive Statement3) Converse Statement4) Inverse Statement5) Is the statement Biconditional?

Workbook page 9

1) H: 3x + 4 = -5C: x = -3

2) H: you take a class in television broadcasting

C: you will film a sporting event

3) If you do not remember the past, then you are condemned to repeat it.

Workbook page 9

4) If two angles are adjacent, then they share a common vertex and a common side.

5) True

6) True

7) True

Workbook page 9

8) Converse: If -8 > 0, then (-8)2 > 0; true.Inverse: If (-8)2 0, then -8 0; true.Contrapositive: If -8 0, then (-8)2 0; false

9) If you are a junior, then you wait on tables.

10) If you wait on tables, then you are a junior.

2.4 Deductive Reasoning

Law of Detachment

Given:If you have a true conditional statement

and the hypothesis occurs… pq is true p is given

Conclusion:Then, the conclusion will also occur.

q is true

Law of Detachment

Given: If three points are collinear, then the points are all on one line. E, F, and G are collinear.

Conclusion: E, F, and G are all on one line.

Example 1:

Law of Detachment

Example 2:Given: If I find $20 in the street, then I’ll take you to the movies. On October 10 I found $20 in the street.Conclusion: I will take you to the movies.

Law of SyllogismGiven:

Two true conditional statements and the conclusion of the first is the

hypothesis of the second.pq and qr

Conclusion: If the hypothesis of the first occurs,

then the conclusion of the second will also occur.

pr

Law of Syllogism

If it rains today, then we will not see our friends.

Example:If it rains today, then we will not have a picnic.

If we do not have a picnic, then we will not see our friends.

Conclusion:

Given: